The greedy crowd and smart leaders: a hierarchical strategy selection game with learning protocol

Abstract

In this paper, a general resource distribution game with a hierarchical structure on the bipartite graph is proposed. In this system, the game is divided into two interacting levels, the agent level and the group level, with negotiations taking place on both levels. Each agent can belong to multiple groups, resulting in a system topology with a bipartite structure. On the agent level, decisions are based on the greedy principle, with the game being a state-based potential game. In contrast, some participants on the group level behave more “smartly” and are more likely to adopt a sophisticated strategy maximizing their personal interest. Strategies on both levels are based on distributed protocols, and the social welfare increases as the system approaches a Nash-equilibrium point. The designed protocols are theoretically analyzed from stability and efficiency. Furthermore, a reinforcement learning algorithm is introduced in the group level, where the smarter players are allowed to refine their strategies in the multi-step decision-making process by learning from historic game outcomes. In theory and according to simulations, agents with the learning behavior improve not only their personal interest but also the efficiency of the systemic resource distribution.